15 research outputs found
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations
Recently, ParaExp was proposed for the time integration of linear hyperbolic
problems. It splits the time interval of interest into sub-intervals and
computes the solution on each sub-interval in parallel. The overall solution is
decomposed into a particular solution defined on each sub-interval with zero
initial conditions and a homogeneous solution propagated by the matrix
exponential applied to the initial conditions. The efficiency of the method
depends on fast approximations of this matrix exponential based on recent
results from numerical linear algebra. This paper deals with the application of
ParaExp in combination with Leapfrog to electromagnetic wave problems in
time-domain. Numerical tests are carried out for a simple toy problem and a
realistic spiral inductor model discretized by the Finite Integration
Technique.Comment: Corrected typos. arXiv admin note: text overlap with arXiv:1607.0036
Shape Optimization of Rotating Electric Machines using Isogeometric Analysis and Harmonic Stator-Rotor Coupling
This work deals with shape optimization of electric machines using
isogeometric analysis. Isogeometric analysis is particularly well suited for
shape optimization as it allows to easily modify the geometry without remeshing
the domain. A 6-pole permanent magnet synchronous machine is modeled using a
multipatch isogeometric approach and rotation of the machine is realized by
modeling the stator and rotor domain separately and coupling them at the
interface using harmonic basis functions. Shape optimization is applied to the
model minimizing the total harmonic distortion of the electromotive force as a
goal functional
Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems
The eddy current problem has many relevant practical applications in science,
ranging from non-destructive testing to magnetic confinement of plasma in
fusion reactors. It arises when electrical conductors are immersed in an
external time-varying magnetic field operating at frequencies for which
electromagnetic wave propagation effects can be neglected.
Popular formulations of the eddy current problem either use the magnetic
vector potential or the magnetic scalar potential. They have individual
advantages and disadvantages. One challenge is related to differential
geometry: Scalar potential based formulations run into trouble when conductors
are present in non-trivial topology, as approximation spaces must be then
augmented with generators of the first cohomology group of the non-conducting
domain.
For all existing algorithms based on lowest order methods it is assumed that
the extension of the graph-based algorithms to high-order approximations
requires hierarchical bases for the curl-conforming discrete spaces. However,
building on insight on de Rham complexes approximation with splines, we will
show in the present submission that the hierarchical basis condition is not
necessary. Algorithms based on spanning tree techniques can instead be adapted
to work on an underlying hexahedral mesh arising from isomorphisms between
spline spaces of differential forms and de Rham complexes on an auxiliary
control mesh
Combined Parameter and Shape Optimization of Electric Machines with Isogeometric Analysis
In structural optimization, both parameters and shape are relevant for the
model performance. Yet, conventional optimization techniques usually consider
either parameters or the shape separately. This work addresses this problem by
proposing a simple yet powerful approach to combine parameter and shape
optimization in a framework using Isogeometric Analysis (IGA). The optimization
employs sensitivity analysis by determining the gradients of an objective
function with respect to parameters and control points that represent the
geometry. The gradients with respect to the control points are calculated in an
analytical way using the adjoint method, which enables straightforward shape
optimization by altering of these control points. Given that a change in a
single geometry parameter corresponds to modifications in multiple control
points, the chain rule is employed to obtain the gradient with respect to the
parameters in an efficient semi-analytical way. The presented method is
exemplarily applied to nonlinear 2D magnetostatic simulations featuring a
permanent magnet synchronous motor and compared to designs, which were
optimized using parameter and shape optimization separately. It is numerically
shown that the permanent magnet mass can be reduced and the torque ripple can
be eliminated almost completely by simultaneously adjusting rotor parameters
and shape. The approach allows for novel designs to be created with the
potential to reduce the optimization time substantially
How to Build the Optimal Magnet Assembly for Magnetocaloric Cooling: Structural Optimization with Isogeometric Analysis
In the search for more efficient and less environmentally harmful cooling
technologies, the field of magnetocalorics is considered a promising
alternative. To generate cooling spans, rotating permanent magnet assemblies
are used to cyclically magnetize and demagnetize magnetocaloric materials,
which change their temperature under the application of a magnetic field. In
this work, an axial rotary permanent magnet assembly, aimed for
commercialization, is computationally designed using topology and shape
optimization. This is efficiently facilitated in an isogeometric analysis
framework, where harmonic mortaring is applied to couple the rotating
rotor-stator system of the multipatch model. Inner, outer and co-rotating
assemblies are compared and optimized designs for different magnet masses are
determined. These simulations are used to homogenize the magnetic flux density
in the magnetocaloric material. The resulting torque is analyzed for different
geometric parameters. Additionally, the influence of anisotropy in the active
magnetic regenerators is studied in order to guide the magnetic flux. Different
examples are analyzed and classified to find an optimal magnet assembly for
magnetocaloric cooling
Principle of pragmatism? The framing of the 1842 Copyright Act
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